A Contribution to the Vector and Tensor Analysis: Course by Zlatko Jankocic

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By Zlatko Jankocic

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Additional info for A Contribution to the Vector and Tensor Analysis: Course Held at the Department for Mechanics of Deformable Bodies September – October 1969

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6. 5) ~. Thus, for the two spaces the difference between cases A and B disappears. We introduce a one-to-one correspondence between the vectors of the two space s X(C) . TX ex t, f. = ')(e )C>J;i. e. e: = X>~i. t. xe J X (6. e t.. asso The requirement that the associated vector of the ciated vector should be the original one (e. g. eX = ei = ez ) e X ) leads to the conclusion that the operators (6.

S. Ahiezer-I. M. Glazman : Teoria linejnih operatorov v Hilbertovom prostranstve, Moskva 1966 K. , Berlin A CONTRIBUTION TO THE VECTOR AND TENSOR ANALYSIS I In a preceding paper [ 1] we developed a simple approach to the vector and tensor algebra, whose basic characte ristic was the equivalence of covariant, the contravariant, bra and ket forms. Based on this feature, is vector and tensor analysis for vector and tensor fields built up in the present paper, the n-dimensional vector spaces being connected with the points of an m-dimensiona l param ete r manifold.

Symbolically we write T = T1 ® ~ 0 ... 0 Tm ' T,1.. L 7 Te X =n m ® xi. :'l the type of the tensor T ' ( 5. 5a) being (5. Sb) The rank of the tensor T is equal to the sum of factor tensor ranks. As an example we write the direct tensor product explicitly ( 5. 6a) the type of the tensor (5. 6a) being (414) = (1 3 13) == (' 1. )+-(•. 1 •. • (5. 6b) Vector and Tensor Algebra 34 Naturally, in the direct tensor product we could allow definite the same cx. valences, when belanging to bra and ket vector spaces, to act one upon an- other according to (1.

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